This approach of modeling the environment also maintains the flexibility to model NV centers in other environments. This means that while we limit ourselves to the choice of a NV center experiencing dipolar coupling to a surrounding electronic spin bath, which results in the stretched exponential parameter \(p=1(2)\)  for the ensemble (single) scenario, the parameter can be modified to model different environments. For example a non-integer value of \(p\)  might suggest the presence of strain gradients, magnetic fields, temperature gradients or other more complex dephasing mechanisms [1]}, these exact values of \(p\)  are well characterised for the single spin under a variety of environments [2]}, [3]}, [4]}
Such modeling approaches have shown tremendous agreement for results involving theory and experiment in single NV centers [3]}, [2]}, [7]}, [8]} and ensembles [1]}, [10]}. In short, by varying the noise parameters, the formalism we present for magnetic field detection can be applied to very different sets of experimental environments.
